Peter Brass

This text closely examines ideas, analysis, and implementation details of data structures as a specialised topic in applied algorithms. It looks at efficient ways to realise query and update operations on sets of numbers, intervals, or strings by various data structures, including: search trees; structures for sets of intervals or piece-wise constant functions; orthogonal range search structures; heaps; union-find structures; dynamization and persistence of structures; structures for strings; and hash tables. Instead of relegating data structures to trivial material used to illustrate object-oriented programming methodology, this is the first volume to show data structures as a crucial algorithmic topic. Numerous code examples in C and more than 500 references make Advanced Data Structures an indispensable text.

Although discrete geometry has a rich history extending more than 150 years, it abounds in open problems that even a high-school student can understand and appreciate. Some of these problems are notoriously difficult and are intimately related to deep questions in other fields of mathematics. But many problems, even old ones, can be solved by a clever undergraduate or a high-school student equipped with an ingenious idea and the kinds of skills used in a mathematical olympiad. Research Problems in Discrete Geometry is the result of a 25-year-old project initiated by the late Leo Moser. It is a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research. Important features include: - More than 500 open problems, some old, others new and never before published - Each chapter divided into self-contained sections, each section ending with an extensive bibliography - A great selection of research problems for graduate students looking for a dissertation topic - A comprehensive survey of discrete geometry, highlighting the frontiers and future of research - More than 120 figures - A preface to an earlier version written by the late Paul Erdos Peter Brass is Associate Professor of Computer Science at the City College of New York. William O. J. Moser is Professor Emeritus at McGill University. Janos Pach is Distinguished Professor at The City College of New York, Research Professor at the Courant Institute, NYU, and Senior Research Fellow at the Rényi Institute,Budapest.

This text closely examines ideas, analysis, and implementation details of data structures as a specialised topic in applied algorithms. It looks at efficient ways to realise query and update operations on sets of numbers, intervals, or strings by various data structures, including: search trees; structures for sets of intervals or piece-wise constant functions; orthogonal range search structures; heaps; union-find structures; dynamization and persistence of structures; structures for strings; and hash tables. Instead of relegating data structures to trivial material used to illustrate object-oriented programming methodology, this is the first volume to show data structures as a crucial algorithmic topic. Numerous code examples in C and more than 500 references make Advanced Data Structures an indispensable text.

Although discrete geometry has a rich history extending more than 150 years, it abounds in open problems that even a high-school student can understand and appreciate. Some of these problems are notoriously difficult and are intimately related to deep questions in other fields of mathematics. But many problems, even old ones, can be solved by a clever undergraduate or a high-school student equipped with an ingenious idea and the kinds of skills used in a mathematical olympiad. Research Problems in Discrete Geometry is the result of a 25-year-old project initiated by the late Leo Moser. It is a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research. Important features include: - More than 500 open problems, some old, others new and never before published - Each chapter divided into self-contained sections, each section ending with an extensive bibliography - A great selection of research problems for graduate students looking for a dissertation topic - A comprehensive survey of discrete geometry, highlighting the frontiers and future of research - More than 120 figures - A preface to an earlier version written by the late Paul Erdos Peter Brass is Associate Professor of Computer Science at the City College of New York. William O. J. Moser is Professor Emeritus at McGill University. Janos Pach is Distinguished Professor at The City College of New York, Research Professor at the Courant Institute, NYU, and Senior Research Fellow at the Rényi Institute,Budapest.